David McCarthy

David McCarthy is a philosopher who uses mathematics to understand ethics. This website explains why that’s not a contradiction. David works at the University of Hong Kong, where he learns from the brightest undergraduates he has ever taught. He enjoys powerlifting and rock climbing, requiring him to be as big as an ox and as light as a fly. That doesn’t make much sense, but his views about ethics do.

David McCarthy

Department of Philosophy
University of Hong Kong
Hong Kong
Email: davidmccarthy1@gmail.com
URL: davidmccarthy.org

Nationality: British / Irish (dual citizenship)

Areas of specialization

Ethics; Decision Theory; Formal Epistemology; Philosophy of Probability


1995 PhD in Philosophy, University of Southern California
1988 MA in Mathematics and Philosophy, University of Oxford

Appointments held

2011-         Associate Professor, University of Hong Kong
2004-2011  Reader, University of Edinburgh
2003-2004  Senior Lecturer, University of Bristol
2000-2003  Lecturer, University of Bristol
1997-2000  Lecturer, University of Melbourne
1997          Lecturer, Monash University
1995-1997  Greenwall Fellow, Johns Hopkins University


McCarthy, D. The Structure of Good, Oxford University Press, under contract. Contact David McCarthy for a copy.


McCarthy, D., Mikkola, K., Thomas, T., Expected utility theory on mixture spaces without the completeness axiom. Journal of Mathematical Economics 97 (2021): 102538. PDF | Abstract
McCarthy, D., Mikkola, K., Thomas, T., Utilitarianism with and without expected utility. Journal of Mathematical Economics 87 (2020): 77-113. Online Article | PDF | Abstract | Discussion
McCarthy, D., Mikkola, K., Continuity and completeness of strongly independent preorders. Mathematical Social Sciences 93 (2018): 141–145. PDF | Abstract | Discussion
McCarthy, D., The priority view. Economics and Philosophy 33(2) (2017): 215–257. PDF | Abstract
McCarthy, D., Distributive equality. Mind 124(496) (2015): 1045–1109. PDF | Abstract
McCarthy, D., Risk-free approaches to the priority view. Erkenntnis 78(2)(2013): 421–49. PDF | Abstract
McCarthy, D., Utilitarianism and prioritarianism II. Economics and Philosophy 24(1) (2008): 1–33. PDF | Abstract
McCarthy, D., Measuring life’s goodness. Philosophical Books 48(4) (2007):303–19. PDF | Abstract
McCarthy, D., Utilitarianism and prioritarianism I. Economics and Philosophy 22(3) (2006): 335–63. PDF | Abstract
McCarthy, D., Intending harm, foreseeing harm and failures of the will. Noûs 36(4) (2002): 622–42. PDF | Abstract
McCarthy, D., Harming and allowing harm. Ethics 110(4) (2000): 749–79 PDF | Abstract
McCarthy, D., Actions, beliefs and consequences. Philosophical Studies 90(1)(1998): 57–77. PDF | Abstract
Arntzenius, F., McCarthy, D., Self-torture and group beneficence. Erkenntnis 47(1) (1997): 129–44. PDF | Abstract
Arntzenius, F., McCarthy, D., The two envelope paradox and infinite expectations. Analysis 57(1) (1997): 42–50. PDF | Abstract
McCarthy, D., Rights, explanation, and risk. Ethics 107(2) (1997): 205–22. PDF | Abstract
McCarthy, D., Liability and risk. Philosophy and Public Affairs 25(3) (1996): 238–62. PDF | Abstract


McCarthy, D., Probability in ethics. In A. Hájek and C. Hitchcock eds. The Oxford Handbook of Philosophy and Probability, Oxford University Press, 2016, 705–37. PDF | Abstract


McCarthy, D., Mikkola, K., Thomas, T., Aggregation for potentially infinite populations without continuity or completeness. arXiv:1911.00872 [econ.TH] (2019). Online Article | PDF | Abstract
McCarthy, D., Mikkola, K., Thomas, T., Representation of strongly independent preorders by vector-valued functions. MPRA Paper No. 80806 (2017). Online Article | PDF | Abstract

Grants & visiting positions

2014 HKU / KCL Fellowship (Hong Kong & UK )
2013-2016 GRF (Hong Kong)
2008 AHRC Research Leave Scheme (UK)
2005 Senior Research Fellow, Philosophy, Probability and Modeling Group, University of Konstanz (Germany)
2003 AHRC Research Leave Scheme (UK) 2000 ARC Large Grant (Australia)



Ethics; decision theory; philosophy of probability; formal epistemology; philosophy of social science; political philosophy; metaphysics; philosophical methods.


As well as the above topics: epistemology; formal logic; game theory.


As well as the above topics: critical thinking as a general education course.



Prof. John Broome, University of Oxford. Email: john.broome@philosophy.ox.ac.uk
Prof. Wlodek Rabinowicz, University of Lund. Email: Wlodek.Rabinowicz@fil.lu.se


Dr. Natalie Gold, Kings College London. Email: natalie.gold@kcl.ac.uk

David McCarthy
Department of Philosophy
University of Hong Kong
Hong Kong

I started life in academia doing a degree in Mathematics at Oxford in the mid 1980s. I switched to Mathematics and Philosophy to avoid some compulsory courses in applied mathematics, with the idea that learning what philosophy was about would be interesting. It turned out to be very interesting, and I fell in love with the subject, thanks to a year of tutorials in metaphysics, philosophy of language and philosophical logic with Simon Blackburn.

I went on to do a PhD in Los Angeles, and after dabbling in metaphysics, logic and set theory, I started working on ethics with Barbara Herman. I found the many of the ideas of contractualism appealing, and whereas Rawls had already started limiting the scope of his contractualism, I was curious to see whether it could be extended to a full-blown ethical theory, providing, for example, a systematic treatment of such things as harming versus allowing harm.

But while I found the contractualist vision appealing, the devil is in the detail, and there were things that bothered me. For one thing, many of the concrete positions seemed either implausible or vague. For example, Rawls’ views about rationality behind the veil of ignorance are unconvincing to say the least, while Scanlon’s account of his distributive alternative to utilitarianism is like defining biology by saying it’s not chemistry or physics.

In the early 2000s I had some ideas about how to develop contractualism, and I realised that I needed some mathematics. Hopelessly lost, I started wandering through the mathematics library. Stumbling on János Azcél’s books on functional equations helped me solve some problems, and a breakthrough came when Derek Parfit passed one of my rambling manuscripts to John Broome, who wrote to me to recommend that I look at the work of John Harsanyi.

Like most recipients of good advice, my response was slow and begrudging. But eventually I began to realise the immense value, not just of Harsanyi’s work, but also of the vast literature in economics that has extended it. But back to Rawls, who thought of moral philosophy as the systematic comparison of different ways of thinking about ethics, requiring the articulation of alternatives to the best known ethical theory, utilitarianism.

This method characterizes a vast body of contemporary ethics, but even if an oracle whispers in your ear that utilitarianism is woefully incorrect, as indeed one gathers from the learned journals, for this to be a useful piece of knowledge, you had better understand what utilitarianism is really saying. This is one reason why Harsanyi’s work is so valuable: it provides the basis for an extremely flexible and powerful defense of utilitarianism.

Understanding and extending Harsanyi’s utilitarianism, and thereby better characterising the alternatives, is therefore central to the Rawlsian project, and this has been my central preoccupation for a decade. It requires some serious mathematics, and since the early 2010s, I have been very fortunate to have collaborated with two first class mathematicians, Kalle Mikkola and Teru Thomas.

It is hardly surprising that ethics requires mathematics. It subsumes subjects like decision theory (rational action), formal epistemology (rational belief), philosophy of probability (uncertainty), game theory (coordination), and no one with even a passing familiarity with those subjects would deny the relevance of mathematics to them. Yet the hostility to mathematical methods by moral philosophers is hard to exaggerate.

Not surprisingly, the greatest hostility typically comes from those who know the least. The existentialists had a word for this: ressentiment. That said, it takes training and patience to be able to read mathematical statements (proofs can almost always be skipped), and the main aim of the blog on this website is to try to provide accessible accounts of standard results and techniques that would be very useful for researchers in ethics to know about.

In 2011 I moved from Edinburgh to the wonderful city of Hong Kong, where I have been happily living ever since. At the University of Hong Kong, I feel hugely privileged to teach and learn from exceptionally bright and respectful undergraduates. In my spare time I enjoy climbing rocks meters from the sea, and being the weakling in the local Strongman / Strong Woman gym.


  • David was recently interviewed in The Reasoner.
  • David will be visiting KCL in May 2019


Utilitarianism, Welfare, and Information

Utilitarianism is often criticized for making assumptions about welfare comparisons that are too strong to be plausible. Roughly speaking, it assumes that all goods can be precisely measured and compared. This criticism applies both to classical utilitarianism, and to Harsanyi’s more sophisticated version.

However, joint work with Kalle Mikkola and Teru Thomas provides a response. Our version of utilitarianism, a generalization of Harsanyi’s, has almost unlimited flexibility when it comes to welfare comparisons. It allows for all kinds of incomparabilities. The post connects this flexibility with uncertainty.

Protected: Formal Epistemology PHIL2900 General

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